The eight-times Super League champions slumped back to joint-bottom once more following yet another defeat.
With just six games remaining, relegation fears simply cannot be eased as Leeds continue to make the same rudimentary errors time and time again.
They were 20-6 behind against Hull FC on Sunday before finally clicking into gear to lead 24-20 – only to then spill the restart and gift their opponents a way back in to win 26-24.
“We make too many mistakes at the minute and you can’t afford to do that,” said Briscoe.
“You have to take your opportunities when you can and we are not doing that at the minute.
“Credit to our boys, we stuck in to get ourselves back in the game in the second half.
“It was just a few too many mistakes and penalties we gave away.
“That makes it hard against the top sides, there’s no doubt about that. We are getting ourselves in the game, but we just can’t get that win at the minute or see a tough game out.”
Ex-England international Briscoe scored two tries against his former club as Leeds threatened to pull off a much-needed win. That saw him reach double figures for the campaign and, given the way in which they were fashioned, it showed Rhinos certainly have potential.
“There were some nice shifts to get the ball to me and some nice lines to create that space,” he said.
“It is nice to get over for a couple of tries, but I would definitely have swapped them for a win.”
Leeds had won two of their previous three games under Richard Agar to offer hope of a late surge up the table.
However, back-to-back defeats at home to Hull KR and Hull has left them in jeopardy once more.
They sit in tenth but level on points with KR, in 11th, and bottom-placed London Broncos.
With no game this weekend, they can turn all their attentions to preparing for Huddersfield Giants who host them on Friday week.
Huddersfield’s win at Hull KR saw them up to eighth – but still only two points off bottom in the heavily congested lower half of the table.
Briscoe, 29, said: “We know what’s going wrong, it’s just a matter of working on that.
“We have got a week off now to concentrate on everything that went wrong.
“We have to take the positives and build on that for what’s an important game at Huddersfield.”